v1 = 4;
v2 = 0;
n = 64;
h = 1/n;
w = 2/3;
k = [1:n/2];
lambda = 1 - 2 * w * sin(k.*pi/2/n).^2;
lambda_ =1 - 2 * w * sin((n-k).*pi/2/n).^2;
c1 = lambda.^(v1+v2) .* sin(k.*pi/2/n).^2;
c2 = lambda.^v1 .* lambda_.^v2 .* sin(k.*pi/2/n).^2;
c3 = lambda_.^v1 .* lambda.^v2 .* cos(k.*pi/2/n).^2;
c4 = lambda_.^(v1+v2) .* cos(k.*pi/2/n).^2;
plot(k,c1,k,c2,k,c3,k,c4);
legend('c1','c2','c3','c4');
xlabel('k');
ylabel('damping coefficient');